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Permutation: n Different Things Taken r at a Time

If the circle...

Question

If the circle $x^{2} + y^{2} + 2 x - 2 y + 4 = 0$ cuts the circle $x^{2} + y^{2} + 4 x + 2 f y + 2 = 0$
orthogonally, then $f =$

A

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B

2

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C

- 1

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D

- 2

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Solution

The correct option is C $- 1$
If two circles cut each other orthogonally then,
$\Rightarrow 2 g_{1} g_{2} + 2 f_{1} f_{2} = c_{1} + c_{2}$
$2 \times (1) (2) + 2 (- 1) \times f = 4 + 2$
$4 - 2 f = 6$
$f = - 1$

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